How do I convert a 3D model into a bas relief using mist?
You can use a Mist pass to generate a height-map, and then use the height-map to control displacement. I'm assuming you want to print this coin, not just to render it, so the displacement is in a modifier, not a texture in a material, which would generate geometry only at render-time.

This example happens to be shooting down Z..


Arrange your model for a vertical shot, camera at (0,0, something),  looking straight down. In this case, Suzanne's ears were too high relative to the other elements, so I scaled her mesh in global Z. (The shot is going to be orthographic, so scaling in Z doesn't move anything in the picture plane)





Check the 'Mist' pass in Render Layers > Passes





In the Render tab, set the Dimensions your desired height-map size: (here, 4096x4096)  We need a high color depth in the output: I find it most convenient to set the Output to  'Open EXR Multilayer', so we can can recover the Mist layer later.. You can also set a 1-frame animation length here.
Set the camera to Orthographic, adjust the orthographic scale to contain your objects, check the 'Mist' display so we can see what we're doing in the next step...





In the 'World' tab, adjust the 0 and 1 levels of the Mist pass (the two dots at the end of the bar), to capture the depths of interest. Set the falloff to 'Linear'.





Shoot a height-map by hitting the 'Animation' button to save out your 1-frame animation. Or, if you shoot a 'Render' still, you will have to save the image out manually. You can see the map by selecting 'Mist' in the 'Select Pass' dropdown in the render window.





Model a blank coin, and subdivide it. Here, I've CtrlF > Grid Filled a circle, and added a rim.
U UV unwrap the model, looking through the camera, with 'Project from View, Bounds'





In the texture tab, load up your heightmap. You can split out the Mist Layer here. Uncheck alpha.





Assign a Simple subsurface modifier and a Displace modifier to the coin, using the texture you've just created, and you're there.




Phew! This took a lot longer to describe than to do.. don't worry.